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Obtaining high-quality images from physical systems, objects, and processes is fundamental for a myriad of areas of science and technology. However, in many situations, the measured images contain defects and/or are accompanied by noise, degrading the quality of the measurement. Recently, a variant of the well-known Talbot self-imaging effect has been shown to redistribute the energy of a spatially periodic collection of images, obtaining output images with increased energy with respect to the input ones. In this work we experimentally demonstrate that such an energy redistribution method has the unique capabilities of increasing the coherent energy level of a periodic set of images over that of the incoherent noise, even allowing images completely buried under noise to be recovered. We further demonstrate that the process can mitigate potential faults of the periodic image structure, including blocked images, spatial jitter, and coherent noise, offering important enhancements (e.g., in regards to the quality of the recovered individual images) in the self-healing capabilities of Talbot self-imaging.Fresnel zone plates are frequently used as focusing and imaging optics in x-ray microscopy, as they provide the ease of use of normal incidence optics. We consider here the effects of tilt misalignment on their optical performance, both in the thin optics limit and in the case of zone plates that are sufficiently thick so that volume diffraction effects come into play. Using multislice propagation, we show that simple analytical models describe the tilt sensitivity of thin zone plates and the thickness at which volume diffraction must be considered, and examine numerically the performance of example zone plates for soft x-ray focusing at 0.5 keV and hard x-ray focusing at 10 keV.Research in laser-plasma interaction, high harmonic generation, and filamentation involves Gaussian beams propagating through inhomogeneous media, where the refractive index varies spatially in both the transverse and longitudinal directions. However, most analytical Gaussian beam solutions to the paraxial wave equation for inhomogeneous media are limited to media with the refractive index only varying quadratically in the transverse direction. In this paper, we present a new class of Gaussian beam solutions for a longitudinally varying medium with a transverse quadratic-index profile. We also highlight a few examples from this class of solutions, which include features such as a one-parameter generalization of the free-space Gaussian beam, beam "collimation," beam self-focusing, and the existence of multiple beam waists.Pupil size is modulated not only by the luminance at the eye position but also by that at the attended location. This study aims to examine whether pupil changes also correspond to the luminance at the spatial location to which the attention is shifted in optokinetic nystagmus. The test stimulus consisted of randomly positioned dots that moved to the left or to the right on a display screen that was bright on one side of the centerline and dark on the other. The results show that pupil size changes in accordance with the luminance at the location to which participants' attention shifts as a result of optokinetic nystagmus (i.e., eye movements in the direction opposite to that of the motion stimulus). This study suggests that pupil size is modulated by the luminance at the location to which attention shifts through unidirectional field motion.Conventional fluorescence polarization microscopy has been largely used to monitor the orientation and the structural information of biomolecules labeled with fluorescence dipoles but suffers from the optical diffraction limit. Here, we put forward a novel algorithm to simultaneously acquire the super-resolution image and the effective orientation distribution information of dipole clusters at corresponding super-resolution. In this paper, the orientation distribution of dipole clusters is statistically modeled by its mean orientation and orientation deviation, which are, respectively, represented by the middle direction and the opening angle of a sector shape. According to this model and microscopy imaging theory, the joint reconstruction algorithm is deduced mathematically in detail based on the conjugate gradient least-squares method. By applying this algorithm to different samples, the reconstructed results prove more than twice the resolution of wide-field images and the orientation distribution information at corresponding spatial resolution. Furthermore, the high accuracy of this algorithm in reconstructing super-resolution orientation distribution information is verified by Monte Carlo simulations.Digital holographic microscopy supplemented with the developed cell segmentation and machine learning and classification algorithms is implemented for quantitative description of the dynamics of cellular necrosis induced by photodynamic treatment in vitro. It is demonstrated that the developed algorithms operating with a set of optical, morphological, and physiological parameters of cells, obtained from their phase images, can be used for automatic distinction between live and necrotic cells. The developed classifier provides high accuracy of about 95.5% and allows for calculation of survival rates in the course of cell death.The moiré effect in 3D objects with planar facets is considered. The projected period of the inclined periodic grating was found. The formula for the period of the moiré patterns in inclined plain surfaces was obtained for objects with arbitrary oriented plain facets, namely, the parallelepiped and the prism (parallel and non-parallel facets). The similarity between the projected period and the moiré period was demonstrated. The direction to the longest moiré pattern in the wedge was found theoretically and observed in experiments. The results can be used in the alignment of flat surfaces.Propagation of a vector vortex optical field (VVOF) with both fractional order of polarization topological charge $m$m and fractional order of vortex topological charge $n$n with spatially variant states of polarization (SoP) in a strongly nonlocal nonlinear medium (SNNM) is studied. The optical field always evolves reciprocally with a cycle of stretch and shrink in a SNNM with dark stripes forming at $z=t\pi z_p$z=tπzp ($t$t denotes an integer number, and $z_p$zp is a parameter that depends on the initial power of the VVOF and the material constant associated with the response function), as a result from the coherent superposition of the vortices with different order of topological charges and weighting coefficients. In particular, the conversions between linear and circular polarization components occur during propagation, and the converted SoP distributions in different propagation distances depend closely on the topological charges and the initial powers. The evolutions of the Stokes parameters of the fractional-order VVOF (FO-VVOF) during propagation in a SNNM show that the spatial distributions of different polarization components are closely related to the topological charges, the initial powers and the propagation distances, implying that the FO-VVOF can be regarded as a superposition of two different fractional-order vortices with orthogonal circular polarization components. These results provide new strategies on tailoring polarization states in a structured optical field with fractional topological charges.A new kind of pulsed beam, which we call a spatially truncated Gaussian pulsed beam, is defined to represent a Gaussian pulsed beam that is diffracted from a semi-infinite hard aperture. The analytical equations for the propagation of the spatially truncated Gaussian pulsed beam through a nonrotationally symmetric paraxial system with second-order dispersion is derived starting from the generalized spatiotemporal Huygens integral. The spatially truncated Gaussian pulsed beam is then combined with the conventional Gaussian pulsed beam decomposition method to enable the modeling of diffraction of a general ultrashort pulse from an arbitrarily shaped hard aperture. The accuracy of the analytical propagation equation derived for the propagation of the truncated Gaussian pulsed beam is evaluated by a numerical comparison with diffraction results obtained using the conventional pulse propagation method based on the Fourier transform algorithm. this website The application of the modified Gaussian pulsed beam decomposition method is demonstrated by propagating an ultrashort pulse after a circular aperture through a dispersive medium and a focusing aspherical lens with large chromatic aberration.This publisher's note corrects an affiliation in J. Opt. Soc. link2 Am. A36, 1585 (2019)JOAOD60740-323210.1364/JOSAA.36.001585.We recently introduced the edge-imaging condition, a necessary condition for all generalized lenses (glenses) [J. Opt. Soc. Am. A33, 962 (2016)JOAOD60740-323210.1364/JOSAA.33.000962] in a ray-optical transformation-optics (RTO) device that share a common edge [Opt. Express26, 17872 (2018)OPEXFF1094-408710.1364/OE.26.017872]. The edge-imaging condition states that, in combination, such glenses must image every point to itself. Here we begin the process of building up a library of combinations of glenses that satisfy the edge-imaging condition, starting with all relevant combinations of up to three glenses. As it grows, this library should become increasingly useful when constructing lens-based RTO devices.We show that $(\textbfE,\textbfH)=(\textbfE_0,\textbfH_0)e^i[k_0S(\textbfr)-\omega t]$(E,H)=(E0,H0)ei[k0S(r)-ωt] is an exact solution to the Maxwell equations in free space if and only if $\\textbfE_0,\textbfH_0, abla S\$E0,H0,∇S form a mutually perpendicular, right-handed set and $S(\textbfr)$S(r) is a solution to both the eikonal and Laplace equations. By using a family of solutions to both the eikonal and Laplace equations and the superposition principle, we define new solutions to the Maxwell equations. We show that the vector Durnin beams are particular examples of this type of construction. link3 We introduce the vector Durnin-Whitney beams characterized by locally stable caustics, fold and cusp ridge types. These vector fields are a natural generalization of the vector Bessel beams. Furthermore, the scalar Durnin-Whitney-Gauss beams and their associated caustics are also obtained. We find that the caustics qualitatively describe, except for the zero-order vector Bessel beam, the corresponding maxima of the intensity patterns.An efficient field-only nonsingular surface integral method to solve Maxwell's equations for the components of the electric field on the surface of a dielectric scatterer is introduced. In this method, both the vector wave equation and the divergence-free constraint are satisfied inside and outside the scatterer. The divergence-free condition is replaced by an equivalent boundary condition that relates the normal derivatives of the electric field across the surface of the scatterer. Also, the continuity and jump conditions on the electric and magnetic fields are expressed in terms of the electric field across the surface of the scatterer. Together with these boundary conditions, the scalar Helmholtz equation for the components of the electric field inside and outside the scatterer is solved by a fully desingularized surface integral method. Compared with the most popular surface integral methods based on the Stratton-Chu formulation or the Poggio-Miller-Chew-Harrington-Wu-Tsai (PMCHWT) formulation, our method is conceptually simpler and numerically straightforward because there is no need to introduce intermediate quantities such as surface currents, and the use of complicated vector basis functions can be avoided altogether.